8-1

Six Sigma Green Belt

Part 8

Case Study

© 2011 IIE and Aft Systems, Inc.

© 2011 IIE and Aft Systems, Inc. 8-2

Case Study

• On the following pages are inspection results on the diameter of a component used in the transmission for a vehicle. Sample “C” came from supplier C. Sample “D” came from supplier D.

• Should the company use supplier C, or supplier D, or both, or neither? (Support with analysis.)

© 2011 IIE and Aft Systems, Inc. 8-3

Specifications

The nominal dimension for this product is 10 units

Tolerance limits are + .5 units making the specifications 9.50 and 10.50

© 2011 IIE and Aft Systems, Inc. 8-4

Supplier C

Lot Avg Range

7-Oct 10.0 9.7 10.0 9.8 9.875 0.3

14-Oct 9.9 10.0 10.2 9.7 9.950 0.5

21-Oct 10.1 10.0 9.9 10.2 10.050 0.3

28-Oct 10.0 9.9 10.1 10.0 10.000 0.2

4-Nov 10.0 9.9 10.0 10.1 10.000 0.2

11-Nov 9.9 10.0 10.0 9.9 9.950 0.1

18-Nov 10.1 10.0 9.9 9.9 9.975 0.2

25-Nov 10.0 9.8 9.9 10.0 9.925 0.2

2-Dec 10.0 10.0 10.1 9.7 9.950 0.4

9-Dec 9.9 10.0 10.0 10.0 9.975 0.1

16-Dec 9.9 10.0 10.1 10.0 10.000 0.2

23-Dec 10.0 10.2 9.8 10.1 10.025 0.4

Average: 9.973 0.258

Sample

© 2011 IIE and Aft Systems, Inc. 8-5

Supplier D

Lot Avg Range

7-Oct 9.6 10.0 10.0 9.5 9.775 0.5

14-Oct 9.5 9.9 10.5 9.6 9.875 1.0

21-Oct 10.5 10.2 10.1 9.7 10.125 0.8

28-Oct 9.9 9.8 10.3 10.5 10.125 0.7

4-Nov 9.7 9.9 10.0 10.3 9.975 0.6

11-Nov 9.6 9.8 10.1 9.8 9.825 0.5

18-Nov 10.4 10.3 9.6 10.4 10.175 0.8

25-Nov 10.1 9.8 9.7 10.2 9.950 0.5

2-Dec 10.1 10.0 10.4 9.9 10.100 0.5

9-Dec 9.5 10.3 10.4 10.0 10.050 0.9

16-Dec 9.7 10.2 10.5 10.2 10.150 0.8

23-Dec 10.0 10.2 10.5 10.1 10.200 0.5

Average: 10.03 0.675

Sample

© 2011 IIE and Aft Systems, Inc. 8-6

Expanded Normal Curve ValuesZ Proportion Z Proportion Z Proportion Z Proportion Z Proportion Z Proportion Z Proportion

3.51 0.00022405 3.82 0.00006673 4.14 0.00001737 4.25 0.00001069 4.57 0.00000244 4.89 0.00000050 5.21 0.00000009

3.52 0.00021577 3.83 0.00006407 4.15 0.00001662 4.26 0.00001022 4.58 0.00000232 4.90 0.00000048 5.22 0.00000009

3.53 0.00020778 3.84 0.00006152 4.16 0.00001591 4.27 0.00000977 4.59 0.00000222 4.91 0.00000046 5.23 0.00000008

3.54 0.00020006 3.85 0.00005906 4.17 0.00001523 4.28 0.00000934 4.60 0.00000211 4.92 0.00000043 5.24 0.00000008

3.55 0.00019262 3.86 0.00005669 4.18 0.00001458 4.29 0.00000893 4.61 0.00000201 4.93 0.00000041 5.25 0.00000008

3.56 0.00018543 3.87 0.00005442 4.19 0.00001395 4.30 0.00000854 4.62 0.00000192 4.94 0.00000039 5.26 0.00000007

3.57 0.00017849 3.88 0.00005223 4.20 0.00001335 4.31 0.00000816 4.63 0.00000183 4.95 0.00000037 5.27 0.00000007

3.58 0.00017180 3.89 0.00005012 4.21 0.00001277 4.32 0.00000780 4.64 0.00000174 4.96 0.00000035 5.28 0.00000006

3.59 0.00016534 3.90 0.00004810 4.22 0.00001222 4.33 0.00000746 4.65 0.00000166 4.97 0.00000033 5.29 0.00000006

3.60 0.00015911 3.91 0.00004615 4.23 0.00001168 4.34 0.00000712 4.66 0.00000158 4.98 0.00000032 5.30 0.00000006

3.61 0.00015310 3.92 0.00004427 4.24 0.00001118 4.35 0.00000681 4.67 0.00000151 4.99 0.00000030 5.31 0.00000005

3.62 0.00014730 3.93 0.00004247 4.25 0.00001069 4.36 0.00000650 4.68 0.00000143 5.00 0.00000029 5.32 0.00000005

3.63 0.00014171 3.94 0.00004074 4.26 0.00001022 4.37 0.00000621 4.69 0.00000137 5.01 0.00000027 5.33 0.00000005

3.64 0.00013632 3.95 0.00003908 4.27 0.00000977 4.38 0.00000593 4.70 0.00000130 5.02 0.00000026 5.34 0.00000005

3.65 0.00013112 3.96 0.00003747 4.28 0.00000934 4.39 0.00000567 4.71 0.00000124 5.03 0.00000025 5.35 0.00000004

3.66 0.00012611 3.97 0.00003594 4.29 0.00000893 4.40 0.00000541 4.72 0.00000118 5.04 0.00000023 5.36 0.00000004

3.67 0.00012128 3.98 0.00003446 4.30 0.00000854 4.41 0.00000517 4.73 0.00000112 5.05 0.00000022 5.37 0.00000004

3.68 0.00011662 3.99 0.00003304 4.31 0.00000816 4.42 0.00000494 4.74 0.00000107 5.06 0.00000021 5.38 0.00000004

3.69 0.00011213 4.00 0.00003167 4.11 0.00001978 4.43 0.00000471 4.75 0.00000102 5.07 0.00000020 5.39 0.00000004

3.70 0.00010780 4.01 0.00003036 4.12 0.00001894 4.44 0.00000450 4.76 0.00000097 5.08 0.00000019 5.40 0.00000003

3.71 0.00010363 4.02 0.00002910 4.13 0.00001814 4.45 0.00000429 4.77 0.00000092 5.09 0.00000018 5.41 0.00000003

3.72 0.00009961 4.03 0.00002789 4.14 0.00001737 4.46 0.00000410 4.78 0.00000088 5.10 0.00000017 5.42 0.00000003

3.73 0.00009574 4.04 0.00002673 4.15 0.00001662 4.47 0.00000391 4.79 0.00000083 5.11 0.00000016 5.43 0.00000003

3.74 0.00009201 4.05 0.00002561 4.16 0.00001591 4.48 0.00000373 4.80 0.00000079 5.12 0.00000015 5.44 0.00000003

3.75 0.00008842 4.06 0.00002454 4.17 0.00001523 4.49 0.00000356 4.81 0.00000075 5.13 0.00000014 5.45 0.00000003

3.76 0.00008496 4.07 0.00002351 4.18 0.00001458 4.50 0.00000340 4.82 0.00000072 5.14 0.00000014 5.46 0.00000002

3.77 0.00008162 4.08 0.00002252 4.19 0.00001395 4.51 0.00000324 4.83 0.00000068 5.15 0.00000013 5.47 0.00000002

3.78 0.00007841 4.09 0.00002157 4.20 0.00001335 4.52 0.00000309 4.84 0.00000065 5.16 0.00000012 5.48 0.00000002

3.79 0.00007532 4.10 0.00002066 4.21 0.00001277 4.53 0.00000295 4.85 0.00000062 5.17 0.00000012 5.49 0.00000002

3.80 0.00007235 4.11 0.00001978 4.22 0.00001222 4.54 0.00000281 4.86 0.00000059 5.18 0.00000011 5.50 0.00000002

3.81 0.00006948 4.12 0.00001894 4.23 0.00001168 4.55 0.00000268 4.87 0.00000056 5.19 0.00000011 5.51 0.00000002

3.82 0.00006673 4.13 0.00001814 4.24 0.00001118 4.56 0.00000256 4.88 0.00000053 5.20 0.00000010 5.52 0.00000002

© 2011 IIE and Aft Systems, Inc. 8-7

Green Belt Cheat Sheet

22 d

MRor

d

R

MeanLSLz

MeanUSLz

l

u

Cp = (Uspec – Lspec)/6

Cpk is the smaller of the following:

Cpku = (Uspec – Mean) / 3

Cpkl = (Mean – Lspec) / 3

RDLCLR

RDUCLR

RAxxLCL

RAxxUCL

3

4

2

2

MRDLCLMR

MRDUCLMR

d

MRxLCLx

d

MRxUCLx

3

4

2

2

3

3

3Level Sigma

Cpk

© 2011 IIE and Aft Systems, Inc. 8-8

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Frequency 15

14

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2

1

© 2011 IIE and Aft Systems, Inc. 8-9

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Frequency 15

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1

© 2011 IIE and Aft Systems, Inc. 8-10

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© 2011 IIE and Aft Systems, Inc. 8-11

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© 2011 IIE and Aft Systems, Inc. 8-12

Sample ID

Averages

Ranges

© 2011 IIE and Aft Systems, Inc. 8-13

Sample ID

Averages

Ranges

© 2011 IIE and Aft Systems, Inc. 8-14

Sample ID

Averages

Ranges

© 2011 IIE and Aft Systems, Inc. 8-15

Sample ID

Averages

Ranges